You’re referring to business personal property and that is its own property type that’s taxed separately. However hotels/apartments have the BPP rolled into the real property values 99% of the time.
in terms of purchase price interplay with it, that’s a major part of skewing purchase price info. Business enterprise value as well. Take a gas station or fast food restaurant, there’s business value with the actual operation, bpp, and the real property of course. lots of money made by experts who do those allocations. As an owner you’d want as much as possible assigned to biz value (not taxable), then bpp (depreciating assets), then finally real property.
THENNN you have to consider fee simple vs leased fee. Technically Texas is (supposed to be) a fee simple assessment state. Ie a tenant property should be valued based on current market rates, not the leases in place. Which is really tricky bc properties are traded on what kind of income they are generating based on sometimes years old lease rates.